Consider the family of lines  x−y−6+λ2x+y+3=0 and  x+2y−4+μ3x−2y−4=0 . If the lines of these two families intersect at right angles to each other, then the locus of their point of intersection is a circle with radius

If all the lines of  L1+λL2=0 are intersecting the lines of L3+μL4=0  in right angle, then the locus of the point of intersection is a circle, whose diameter end points are points of intersections of both family of lines. The point of intersection of the lines x−y−6=0,  2x+y+3=0  is  1,−5 and the point of intersection of the lines  x+2y−4=0,3x−2y−4=0  is  2,1Therefore, the radius of the locus of point of intersection is half of the distance between the points 1,−5  and   2,1Hence, the radius . r=122−12+−5−12=3.04